Problem: Simplify the following expression: $r = \dfrac{q^2 - 13q + 40}{q - 8} $
First factor the polynomial in the numerator. $ q^2 - 13q + 40 = (q - 8)(q - 5) $ So we can rewrite the expression as: $r = \dfrac{(q - 8)(q - 5)}{q - 8} $ We can divide the numerator and denominator by $(q - 8)$ on condition that $q \neq 8$ Therefore $r = q - 5; q \neq 8$